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Popular >

simplify ln((e^ρ)/(1+e^ρ))

Solution

simplify

ln (\frac{e ^{ρ}}{1 + e ^{ρ}})

Solution

ρ - ln (1 + e^{ρ})

Solution steps

ln (\frac{e ^{ρ}}{1 + e ^{ρ}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{e ^{ρ}}{1 + e ^{ρ}}) = ln (e^{ρ}) - ln (1 + e^{ρ})

= ln (e^{ρ}) - ln (e^{ρ} + 1)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{ρ}) = ρ ln (e)

= ρ ln (e) - ln (1 + e^{ρ})

ρ ln (e) = ρ

= ρ - ln (e^{ρ} + 1)

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Frequently Asked Questions (FAQ)

What is ln((e^ρ)/(1+e^ρ)) ?
The solution to ln((e^ρ)/(1+e^ρ)) is ρ-ln(1+e^ρ)